• Journal of the Society of Naval Architects of Korea
• /
• v.58 no.6
• /
• pp.348-357
• /
• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• Advances in nano research
• /
• v.10 no.5
• /
• pp.423-435
• /
• 2021

This paper examines the thermal post-buckling behaviors of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical panels which possess in-plane negative Poisson's ratio (NPR) and rest on an elastic foundation. A panel consists of GRMMC layers of piece-wise varying graphene volume fractions to obtain functionally graded (FG) patterns. Based on the MD simulation results, the GRMMCs exhibit in-plane NPR as well as temperature-dependent material properties. The governing equations for the thermal post-buckling of panels are based on the Reddy's third order shear deformation shell theory. The von Karman nonlinear strain-displacement relationship and the elastic foundation are also included. The nonlinear partial differential equations for GRMMC laminated cylindrical panels are solved by means of a singular perturbation technique in associate with a two-step perturbation approach and in the solution process the boundary layer effect is considered. The results of numerical investigations reveal that the thermal post-buckling strength for (0/90)_5T GRMMC laminated cylindrical panels can be enhanced with an FG-X pattern. The thermal post-buckling load-deflection curve of 6-layer (0/90/0)_S and (0/90)_3T panels of FG-X pattern are higher than those of 10-layer (0/90/0/90/0)_S and (0/90)_5T panels of FG-X pattern.

• Steel and Composite Structures
• /
• v.46 no.4
• /
• pp.553-563
• /
• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Structural Engineering and Mechanics
• /
• v.89 no.1
• /
• pp.13-22
• /
• 2024

The nonlinear snap-through buckling of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) curved tubes is analytically investigated in this research. It is assumed that the FG-CNTRC curved tube is supported on a three-parameter nonlinear elastic foundation and is subjected to the uniformly distributed pressure and thermal loads. Properties of the curved nanocomposite tube are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite tube are temperature-dependent. The governing equations of the curved tube are obtained using a higher-order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved tube. Equations of motion are solved using the two-step perturbation technique for nanocomposite curved tubes which are simply-supported and clamped. Closed-form expressions are provided to estimate the snap-buckling resistance of FG-CNTRC curved pipes rested on nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of the distribution pattern and volume fraction of CNTs, thermal field, foundation stiffnesses, and geometrical parameters on the instability of the curved nanocomposite tube.

• Journal of the Korean earth science society
• /
• v.37 no.2
• /
• pp.107-116
• /
• 2016

Stability of the barotropic Rossby-Haurwitz wave is investigated using the numerical models on the global domain. The Rossby-Haurwitz wave under investigation is composed of the basic zonal flow of super-rotation and a finite amplitude spherical harmonic wave. The Rossby-Haurwitz wave is given as either steady or unsteady wave by adjusting the strength of the super-rotating zonal flow. Stability as well as the growth rate of the wave in the numerical simulation is determined by comparing the perturbation amplitude at two different time stages. Unstable modes of the Rossby-Haurwitz wave exhibited a horizontal structure composing of various zonal-wavenumber components. The vorticity perturbation for some modes showed a discontinuity around the area of weak flow, which was found robust regardless of the horizontal resolution of the model. Fourier finite element model was shown to generate the unstable mode in earlier stage of the time integration due to less accuracy compared to the spherical harmonic spectral model. Taking the overall accuracy of the models into consideration, the time by which the unstable mode begin to dominate over the spherical harmonic wave was estimated.

• Computers and Concrete
• /
• v.32 no.1
• /
• pp.99-117
• /
• 2023

The crack under the influence of the higher intensities of the stresses grows and the structure gets collapsed with the time when the crack length reaches to critical value. Therefore, the fracture behavior of a structure in terms of stress intensity factors (SIF) becomes important to determine the remaining fracture strength and capacity of material and structure for avoiding catastrophic failure, increasing safety and further improvement in the design. The robustness of the method has been demonstrated by comparing the numerical results with analytical and experimental results of some problems. XFEM is used to model cracks and holes in structures and predict their strength and reliability under service conditions. Further, XFEM is extended with a stochastic method for predicting the sensitivity in terms of output COVs and fracture strength in terms of mean values of stress intensity factors (SIFs) of a structure with discontinuities (cracks and holes) under tensile loading condition with input individual and combined randomness in different system parameters. In stochastic technique, the second order perturbation technique (SOPT) has been used for the predicting the fracture behavior of the structures. The stochastic/perturbation technique is also known as Taylor series expansion method and it provides the reliable results if the input randomness is less than twenty percentage. From the present numerical analysis it is observed that, the crack tip near to the hole is under the influence of the stress concentration and the variational effect of the input random parameters on the crack tip in terms of the SIFs are lesser so the COVs are the less sensitive. The COVs of mixed mode SIFs are the most sensitive for the crack angles (α=45° to 90°) for all the values of c₁ and d₁. The plate with the shorter distance between hole and crack is the most sensitive with all the crack angles but the crack tip which is much nearer to the hole has the highest sensitivity.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.39-53
• /
• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.1
• /
• pp.52-63
• /
• 1983

The purpose of the study is to find development of contact area, contact pressure and friction forces occurring at joints or connection areas inbetween structural members or mechanical parts. The problem has a pair of difficulties intrinsically; a constraint of displacement due to contact, and presence of work term by nonconservative friction force in the variational principle of the problem. Because of these difficulties, the variational principle remains in the form of inequality. It is resolved by penalty method and perturbation method making the inequality to an equality which is proper for computational purposes. A contact problem without friction is solved to find contact area and contact pressure, which are to be used as data for the analysis of the friction problem using perturbed variational principle. For numerical experiments, a Hertz problem, a rigid punch problem, and the latter one with friction effects are solved using $Q_2$-finite elements.

• 한국연소학회:학술대회논문집
• /
• 2012.11a
• /
• pp.5-7
• /
• 2012

This study presents relations between the time lag and interaction index of the impinging-jet injectors using time lag model in a model chamber. To analyze the response of the flame, 5% amplitude of oxidizer velocity is artificially perturbed at a resonance frequency. At the mixing point of fuel and oxidizer, which determines the characteristic length, the relationship between velocity perturbation and heat release rate is quantified by combustion parameters of interaction index and time lag. As the improved method to apply the time-lag, the method using the average velocity obtained from numerical results is suggested.

• Structural Engineering and Mechanics
• /
• v.59 no.4
• /
• pp.671-682
• /
• 2016

In this paper, a new analytical approach has been presented for solving nonlinear conservative oscillators. Variational approach leads us to high accurate solution with only one iteration. Two different high nonlinear examples are also presented to show the application and accuracy of the presented approach. The results are compared with numerical solution using runge-kutta algorithm in different figures and tables. It has been shown that the variatioanl approach doesn't need any small perturbation and is accurate for nonlinear conservative equations.